No Sengoku pushing Garp down woke him up from his rage and Garp was still conflicted between sides to choose while he loves Ace and Luffy as his grandchildren he is and will always be a navy soldier at heart and he knew that attacking either Sengoku or Sakazuki would cost him his status. Hence the reason why Sengoku asked Garp if he had gone mad.
Also it makes no sense that Garp would get weaker than Sengoku if anything it's Sengoku who would have been weakened as he got older since Sengoku had a lot less time to train due to his position.
As for Garp being able to throw Sengoku off...yes I'll admit that's speculation but considering Garp was still able to move his head with no effort despite Sengoku holding down shows he wasn't even trying to get back up.
Another thing is if your assuming Garp isn't stronger than Sengoku purely because Sengoku was able to hold him down then your also assuming that Garp wouldn't fight back despite his anger at Sakazuki.
So let me ask you do you really think Garp is scared of Sengoku to the point he would only not fight back out of fear of Sengoku? No. The reason Garp didn't fight back was because Garp wasn't interested in fighting Sengoku he wanted to fight Sakazuki that's why he didn't fight back.
Also considering this logic that if Garp never fought back that means he's weaker then the same logic could have been applied to Luffy and Bellamy before Luffy beat him in one punch however before this Luffy let Bellamy beat him up without fighting back and as we saw Luffy was able to one shot Bellamy...I guess basically the point here is just because someone doesn't fight back it doesn't mean their not stronger.
But he he had killing intent.
He wanted to kill Sakazuki. Meaning he would have done anything to kill him.
And him being slammed to the floor woke him up from his rage?
That is speculation.
However, Garp said it himself that if Sengoku didn't hold him down he would kill Sakazuki.
The fact he had to put effort to keep him on the floor implies Garp was struggling also?
Yes?
And, no. Ofc Garp isnt scared of Sengoku to the point they wouldnt fight.
Imo, they are literally the same strength. Except Sengoku is slightly more.
If they fought anyone imo the outcome would be the same for both men.
But when you pit them against each other, Sengoku is that bit stronger.